(see e.g., [1]}). Notice that one can assume in (REF ) that the functions \(f_i\)  are \(C^1\) , since Lipschitz functions are a.e. differentiable. By the Besicovitch-Marstrand-Mattila Theorem ([1]} a Borel set \(K\subset \mathbb {R}^2\)  with \(\mathcal {H}^1(K)<+\infty \)  is \(\mathcal {H}^1\) -rectifiable if and only if
\(\theta ^*(K,x)=\theta _*(K,x) =1\)  for \(\mathcal {H}^1\) -a.e. \(x\in K,\)  where
\(\theta ^*(K,x):=\limsup \limits _{r\rightarrow 0^+} \frac{\mathcal {H}^1(B_r(x)\cap K)}{2r}\quad \text{and}\quad \theta _*(K,x):=\liminf \limits _{r\rightarrow 0^+} \frac{\mathcal {H}^1(B_r(x)\cap K)}{2r}.\) 
